75 lines
1.9 KiB
Java
75 lines
1.9 KiB
Java
import adder from "./adder.js";
|
||
import {atan2, cos, quarterPi, radians, sin, tau} from "./math.js";
|
||
import noop from "./noop.js";
|
||
import stream from "./stream.js";
|
||
|
||
export var areaRingSum = adder();
|
||
|
||
var areaSum = adder(),
|
||
lambda00,
|
||
phi00,
|
||
lambda0,
|
||
cosPhi0,
|
||
sinPhi0;
|
||
|
||
export var areaStream = {
|
||
point: noop,
|
||
lineStart: noop,
|
||
lineEnd: noop,
|
||
polygonStart: function() {
|
||
areaRingSum.reset();
|
||
areaStream.lineStart = areaRingStart;
|
||
areaStream.lineEnd = areaRingEnd;
|
||
},
|
||
polygonEnd: function() {
|
||
var areaRing = +areaRingSum;
|
||
areaSum.add(areaRing < 0 ? tau + areaRing : areaRing);
|
||
this.lineStart = this.lineEnd = this.point = noop;
|
||
},
|
||
sphere: function() {
|
||
areaSum.add(tau);
|
||
}
|
||
};
|
||
|
||
function areaRingStart() {
|
||
areaStream.point = areaPointFirst;
|
||
}
|
||
|
||
function areaRingEnd() {
|
||
areaPoint(lambda00, phi00);
|
||
}
|
||
|
||
function areaPointFirst(lambda, phi) {
|
||
areaStream.point = areaPoint;
|
||
lambda00 = lambda, phi00 = phi;
|
||
lambda *= radians, phi *= radians;
|
||
lambda0 = lambda, cosPhi0 = cos(phi = phi / 2 + quarterPi), sinPhi0 = sin(phi);
|
||
}
|
||
|
||
function areaPoint(lambda, phi) {
|
||
lambda *= radians, phi *= radians;
|
||
phi = phi / 2 + quarterPi; // half the angular distance from south pole
|
||
|
||
// Spherical excess E for a spherical triangle with vertices: south pole,
|
||
// previous point, current point. Uses a formula derived from Cagnoli’s
|
||
// theorem. See Todhunter, Spherical Trig. (1871), Sec. 103, Eq. (2).
|
||
var dLambda = lambda - lambda0,
|
||
sdLambda = dLambda >= 0 ? 1 : -1,
|
||
adLambda = sdLambda * dLambda,
|
||
cosPhi = cos(phi),
|
||
sinPhi = sin(phi),
|
||
k = sinPhi0 * sinPhi,
|
||
u = cosPhi0 * cosPhi + k * cos(adLambda),
|
||
v = k * sdLambda * sin(adLambda);
|
||
areaRingSum.add(atan2(v, u));
|
||
|
||
// Advance the previous points.
|
||
lambda0 = lambda, cosPhi0 = cosPhi, sinPhi0 = sinPhi;
|
||
}
|
||
|
||
export default function(object) {
|
||
areaSum.reset();
|
||
stream(object, areaStream);
|
||
return areaSum * 2;
|
||
}
|